This type of phase-modulated fiber optic gyroscope derives the angular velocity of rotation on the following principle:
When a rotation at an angular velocity is applied in the optical path, a phase difference 0 due to Sagnac effect occurs with the light propagating clockwise and counterclockwise through the optical path. At this time, the following equation is formed between angular velocity .OMEGA. and phase difference .DELTA..theta.: EQU .DELTA..theta.=(8.pi.NA/.lambda.c).OMEGA. (1)
where A is an area surrounding the optical path, C is a light velocity within a vacuum, .lambda. is a waveform within a vacuum, and N is the number of turns.
If the phase modulator provides a modulated voltage f(t) expressed by the following equation: EQU f(t)=b sin .omega.mt (2)
where b is a modulation amplitude, and .omega.m is a modulation angular frequency, then a phase difference .phi. in phase modulation occurs between clockwise light and counterclockwise light passing through the optical path. EQU .phi.=.omega.m.tau.=nl.omega.m/c=2.pi.fmnl/c (3)
where .tau. is a passage time of light, l is a fiber length, n is a refractive index, and fm is a modulation frequency.
If a light output of the signal generating section is converted into an electric signal by a photoelectric converter, then; ##EQU1## where Jn (n=0, 1, 2 . . .) is Bessel function.
In equation (4), .DELTA..theta. is obtained by extracting basic frequency component S1 and second higher harmonic component S2. EQU .DELTA..theta.=tan.sup.-1 [J2(.xi.)/J1(.xi.).multidot.S1/S2](5) EQU .xi.=2b sin (o/2)
According to equation (5), the value of .DELTA..theta. is indefinite but may be determined by checking the signs of S1 and S2.
The constant term J2(.xi.)/J1(.xi.) is maintained constant by controlling .xi.=2bsin(.phi./2) to render constant the ratio between the second higher harmonic component S2 and fourth higher harmonic component S4; EQU S2/S4=J2(.xi.)/J4(.xi.) (6)
More particularly, the basic modulation frequency component and a plurality of higher modulation harmonic components are extracted from the output signal of the signal generating section. By controlling the drive voltage for the phase modulator to put the amplitude ratios among the plurality of components to a predetermined value, compensation is made for variations in scale factor due to variations and the like in polarization inside the optical fiber resulting from environmental variations such as in temperature and pressure.
In the conventional analog system, the signal processing section includes a plurality of synchronized wave detecting circuits (also called lock-in amplifiers) corresponding to the respective frequency components and arranged downstream of the photoelectric converter in order to extract the basic modulation frequency component and the plurality of higher modulation frequency components. Based on outputs of the synchronized wave detecting circuits, the angular velocity is calculated and the drive voltage is controlled for the phase modulator.
According to the above circuit construction, however, stability of the synchronized wave detecting circuits has great influences on the precision of angular velocity in compensating for variations in the scale factor.
That is, with the synchronized wave detecting circuits, compensating precision may deteriorate as a result of variations or time-dependent changes due to temperature characteristics of the output voltage since analog signals are involved. Consequently, the direction of rotation as derived and the angular velocity calculated lack in reliability.
Further, a step of adjusting gains and the like must be taken initially for the plurality of synchronized wave detecting circuits. Adjusting errors occurring then greatly affects the compensating precision.